Catalan数在一类特殊的数学结构计数的应用  

Applications of Catalan Number in a Special Mathematical Structure Counting

作　　者：耿康 晁福刚[1] 任韩[1,2] 

机构地区：[1]华东师范大学数学系,上海 [2]上海市核心数学与实践重点实验室,上海

出　　处：《应用数学进展》2016年第3期381-389,共9页Advances in Applied Mathematics

基　　金：上海市科学技术委员会的资助,资助课题编号为13dz2260400;同时受到中国国家自然科学基金项目资助(项目批准号:11171114).

摘　　要：Catalan数是指通项公式为 的序列中的 这些数,其最早是由我国清代数学家明安图开始研究的。本文运用Catalan数与生成函数法来解决一类特殊数学结构的计数问题,构造出该数学结构解个数的显性表达式。最后还给出了该数学结构计数问题的另一种解决方案,从另一个角度也利用了广义的Catalan数来解决问题。Catalan number is an important counting function in the combination of a counting theory. It’s general formula: . It was first used by the mathematician Antu in Qing dynasty. The paper uses the method of Catalan number and generating function to solve a class of problems counting the special mathematical structure and constructs the explicit expression of the solution of the mathematical structure. Finally, the paper gives another solution of the mathematical structure counting problem and also makes use of generalized Catalan number from another angle to solve the problem.

关 键 词：CATALAN数 组合计数 生成函数法 

分 类 号：O1[理学—数学]